Question

Asked Dec 2, 2019

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For the function given below, find a formula for the Riemann sum obtained by dividing the interval [

0

0,

2

2] into n equal subintervals and using the right-hand endpoint for each

c Subscript k

ck. Then take a limit of this sum as

n right arrow infinity

n → ∞ to calculate the area under the curve over [

0

0,

2

2].

f left parenthesis x right parenthesis equals x squared plus 3

f(x)=x2+3

Write a formula for a Riemann sum for the function

f left parenthesis x right parenthesis equals x squared plus 3

f(x)=x2+3 over the interval [

0

0,

2

2].

Step 1

Given the interval [0,2] is to be divided into n subintervals and right-hand endpoint for each interval is to be used. The function is:

Dividing the interval into subintervals:

So the right end points are given by:

The Riemann Sum for a function is given by:

Where *x*_{1}, *x*_{2}, *x*_{3}… are the endpoints considered.

Step 2

Using the above formula, the R...

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